Paper Number
RS8 

Session
Techniques and Methods: Rheometry & Spectroscopy/Microscopy

Title
Kramers-Kronig relations for nonlinear rheology

Presentation Date and Time
October 11, 2022 (Tuesday) 1:50

Track / Room
Track 6 / Mayfair

Authors (Click on name to view author profile)

1. Shanbhag, Sachin (Florida State University, Scientific Computing)
2. Joshi, Yogesh M. (Indian Institute of Technology, Chemical Engineering)

Author and Affiliation Lines (in printed abstract book)
Sachin Shanbhag¹ and Yogesh M. Joshi^2
1Scientific Computing, Florida State University, Tallahassee, FL 32306; ²Chemical Engineering, Indian Institute of Technology, Kanpur, Uttar Pradesh 208016, India

Speaker / Presenter 
Shanbhag, Sachin

Keywords
theoretical methods; computational methods

Text of Abstract
In linear rheology, Kramers-Kronig relations (KKR) relate the real and imaginary parts of the complex modulus by appealing to the principle of causality. We use the multiple integral generalization of the Boltzmann superposition principle for nonlinear rheology to derive a general nonlinear KKR for the n-th order complex modulus. Setting n=3, we obtain KKR for medium amplitude parallel superposition (MAPS) rheology. A special case of MAPS is medium amplitude oscillatory shear (MAOS); we obtain MAOS KKR for the third-harmonic MAOS modulus G^*₃₃; however, no such KKR exists for the first harmonic MAOS modulus G^*₃₁. We discuss the practical implications for MAOS KKR, and propose a test to validate experimental data. This test, called the SMEL test, attempts to fit data to a linear combination of MAOS Maxwell elements leveraging a statistical technique called LASSO regression. It works well on a broad range of materials and models, and successfully copes with data that are noisy, or confined to a narrow frequency range.